The construction of smooth spatial paths with Pythagorean-hodograph (PH) quintic splines is proposed. To facilitate real-time computations, an efficient
local
data stream interpolation algorithm is ...introduced to successively construct each spline segment as a quintic PH biarc interpolating second- and first-order Hermite data at the initial and final end-point, respectively. A
C
2
smooth connection between successive spline segments is obtained by taking the locally required second-order derivative information from the previous segment. Consequently, the data stream spline interpolant is globally
C
2
continuous and can be constructed for arbitrary
C
1
Hermite data configurations. A simple and effective selection of the free parameters that arise in the local interpolation problem is proposed. The developed theoretical analysis proves its fourth approximation order while a selection of numerical examples confirms the same accuracy for the spline extension of the scheme. In addition, the performances of the method are also validated by considering its application to point stream interpolation with automatically generated first-order derivative information.
This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of ...available spline technologies for the local resolution of possible singularities as well as the state-of-the-art formulation of convergence and quasi-optimality of adaptive algorithms for both the finite element method and the boundary element method in the frame of isogeometric analysis.
The study of marine Lagrangian transport holds significant importance from a scientific perspective as well as for practical applications such as environmental-pollution responses and prevention ...(e.g., oil spills, dispersion/accumulation of plastic debris, etc.). In this regard, this concept paper introduces the Smart Drifter Cluster: an innovative approach that leverages modern "consumer" IoT technologies and notions. This approach enables the remote acquisition of information on Lagrangian transport and important ocean variables, similar to standard drifters. However, it offers potential benefits such as reduced hardware costs, minimal maintenance expenses, and significantly lower power consumption compared to systems relying on independent drifters with satellite communication. By combining low power consumption with an optimized, compact integrated marine photovoltaic system, the drifters achieve unlimited operational autonomy. With the introduction of these new characteristics, the Smart Drifter Cluster goes beyond its primary function of mesoscale monitoring of marine currents. It becomes readily applicable to numerous civil applications, including recovering individuals and materials at sea, addressing pollutant spills, and tracking the dispersion of marine litter. An additional advantage of this remote monitoring and sensing system is its open-source hardware and software architecture. This fosters a citizen-science approach, enabling citizens to replicate, utilize, and contribute to the improvement of the system. Thus, within certain constraints of procedures and protocols, citizens can actively contribute to the generation of valuable data in this critical field.
The construction of suitable mesh configurations for spline models that provide local refinement capabilities is one of the fundamental components for the analysis and development of adaptive ...isogeometric methods. We investigate the design and implementation of refinement algorithms for hierarchical B-spline spaces that enable the construction of locally graded meshes. The refinement rules properly control the interaction of basis functions at different refinement levels. This guarantees a bounded number of nonvanishing (truncated) hierarchical B-splines on any mesh element. The performances of the algorithms are validated with standard benchmark problems.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
guarantees for the existence of solutions in all cases, although existence is demonstrated for the asymptotic case of densely-sampled data from a smooth curve. Modulation of the hodograph by a scalar ...polynomial is proposed as a means of introducing additional degrees of freedom, in cases where solutions to the end-point interpolation problem are not found. The methods proposed herein are expected to find important applications in exactly specifying rigid-body motions along curved paths, with minimized rotation, for animation, robotics, spatial path planning, and geometric sweeping operations.
The construction of classical hierarchical B-splines can be suitably modified in order to define locally supported basis functions that form a partition of unity. We will show that this property can ...be obtained by reducing the support of basis functions defined on coarse grids, according to finer levels in the hierarchy of splines. This truncation not only decreases the overlapping of supports related to basis functions arising from different hierarchical levels, but it also improves the numerical properties of the corresponding hierarchical basis — which is denoted as truncated hierarchical B-spline (THB-spline) basis. Several computed examples will illustrate the adaptive approximation behavior obtained by using a refinement algorithm based on THB-splines.
► A normalized hierarchical tensor–product B-spline basis is proposed. ► The construction relies on a truncation mechanism of coarse basis functions. ► The local refinement property is illustrated by an adaptive approximation strategy. ► Sparsity and condition numbers of the related matrices are studied experimentally.
In the present work we introduce a complete set of algorithms to efficiently perform adaptive refinement and coarsening by exploiting truncated hierarchical B-splines (THB-splines) defined on ...suitably graded isogeometric meshes, that are called admissible mesh configurations. We apply the proposed algorithms to two-dimensional linear heat transfer problems with localized moving heat source, as simplified models for additive manufacturing applications. We first verify the accuracy of the admissible adaptive scheme with respect to an overkilled solution, for then comparing our results with similar schemes which consider different refinement and coarsening algorithms, with or without taking into account grading parameters. This study shows that the THB-spline admissible solution delivers an effective discretization for what concerns not only the accuracy of the approximation, but also the (reduced) number of degrees of freedom per time step. In the last example we investigate the capability of the algorithms to approximate the thermal history of the problem for a more complicated source path. The comparison with uniform and non-admissible hierarchical meshes demonstrates that also in this case our adaptive scheme returns the desired accuracy while strongly improving the computational efficiency.
•A complete set of algorithms to perform adaptive refinement and coarsening.•Truncated hierarchical B-splines (THB-splines) defined on suitably graded meshes.•We apply the proposed algorithms to linear heat transfer problems.•THB-spline admissible solution delivers an effective discretization.•Our algorithms strongly improve computational efficiency.
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